Permanence for a class of nonlinear difference systems
A class of nonlinear difference systems is considered in this paper. By exploring the relationship between this system and a correspondent first-order difference system, some permanence results are obtained.
- K. Gopalsamy and I. K. C. Leung, “Delay induced periodicity in a neural netlet of excitation and inhibition,” Physica D. Nonlinear Phenomena, vol. 89, no. 3-4, pp. 395–426, 1996.
- K. Gopalsamy and I. K. C. Leung, “Convergence under dynamical thresholds with delays,” IEEE Transactions on Neural Networks, vol. 8, no. 2, pp. 341–348, 1997.
- R. Kuhn and J. L. van Hemmen, Temporal Association: Models of Neural Networks, edited by E. Domany, J. L. van Hemmen, and K. Schulten, Physics of Neural Networks, Springer, Berlin, 1991.
- G. Papaschinopoulos and C. J. Schinas, “Stability of a class of nonlinear difference equations,” Journal of Mathematical Analysis and Applications, vol. 230, no. 1, pp. 211–222, 1999.
- S. G. Ruan and J. Wei, “Periodic solutions of planar systems with two delays,” Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, vol. 129, no. 5, pp. 1017–1032, 1999.
- H. Sedaghat, “A class of nonlinear second order difference equations from macroeconomics,” Nonlinear Analysis. Theory, Methods & Applications, vol. 29, no. 5, pp. 593–603, 1997.
- H. Sedaghat, “Bounded oscillations in the Hicks business cycle model and other delay equations,” Journal of Difference Equations and Applications, vol. 4, no. 4, pp. 325–341, 1998.
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